The quantum simulation of quantum chemistry is a promising application of quantum computers. However, for N molecular orbitals, the \({\mathcal{O}}({N}^{4})\) gate complexity of performing Hamiltonian and unitary Coupled Cluster Trotter steps makes simulation based on such primitives challenging. We substantially reduce the gate complexity of such primitives through a two-step low-rank factorization of the Hamiltonian and cluster operator, accompanied by truncation of small terms. Using truncations that incur errors below chemical accuracy allow one to perform Trotter steps of the arbitrary basis electronic structure Hamiltonian with \({\mathcal{O}}({N}^{3})\) gate complexity in small simulations, which reduces to \({\mathcal{O}}({N}^{2})\) gate complexity in the asymptotic regime; and unitary Coupled Cluster Trotter steps with \({\mathcal{O}}({N}^{3})\) gate complexity as a function of increasing basis size for a given molecule. In the case of the Hamiltonian Trotter step, these circuits have \({\mathcal{O}}({N}^{2})\) depth on a linearly connected array, an improvement over the \({\mathcal{O}}({N}^{3})\) scaling assuming no truncation. As a practical example, we show that a chemically accurate Hamiltonian Trotter step for a 50 qubit molecular simulation can be carried out in the molecular orbital basis with as few as 4000 layers of parallel nearest-neighbor two-qubit gates, consisting of fewer than 10⁵ non-Clifford rotations. We also apply our algorithm to iron–sulfur clusters relevant for elucidating the mode of action of metalloenzymes.

量子化学的量子模拟是量子计算机的有前途的应用。但是，对于N个分子轨道，执行哈密顿量和unit合簇簇托特步的\（{\ mathcal {O}}（{N} ^ {4}）\）门的复杂性使得基于此类原语的仿真具有挑战性。我们通过哈密顿量和簇运算符的两步低秩分解，并伴随小项的截断，来大大降低此类图元的门复杂度。使用会导致低于化学精度的误差的截断法，可以在小型模拟中执行具有\（{\ mathcal {O}}（{N} ^ {3}）\）门复杂度的任意基础电子结构哈密顿量的Trotter步骤，从而降低了到\（{\ mathcal {O}}（{N} ^ {2}）\）渐进状态下的门复杂度；以及gate \（{\ mathcal {O}}（{N} ^ {3}）\）门的复杂unit合簇簇状托特步数随给定分子基础尺寸的增加而变化。在哈密顿量的步骤中，这些电路在线性连接的数组上具有\（{\ mathcal {O}}（{N} ^ {2}）\）深度，比\（{\ mathcal {O }}（{N} ^ {3}）\）缩放，假定没有截断。作为一个实际的例子，我们表明，可以在分子轨道的基础上，利用多达4000层平行的最近邻二量子位门（少于10层），在分子轨道上进行化学上精确的哈密顿Trotter步骤，用于50量子位的分子模拟⁵非Clifford旋转。我们还将算法应用于与阐明金属酶作用方式有关的铁硫簇。